The Taylor Swift song 'Tim Mcgraw': On one hand the narrator and her boyfriend spent an idyllic summer together. On the other hand, the boyfriend is now gone forever and the narrator only has a memory left.
In the Say Anything... song "Death for my Birthday" the narrator spends the entirety of his (wonderful) life praying for death and being miserable. When he finally gets what he wants, he has a moment of reflection before he dies and wishes he had more time to enjoy all of the things he had.
Despite not being program music, Havergal Brian's "Gothic" Symphony has a sort of Bittersweet Ending.
Martina McBride's Concrete Angel definitely has a bittersweet ending (especially if you watch the music video). The poor abused girl ends up dying, but she flies up to a place where she's loved. The ending of the music video shows her little ghost self playing with a group of other children.
The Rhapsody of Fire story of the Emerald Sword Saga, as told on their first five albums. Akron and his army are defeated and peace is returning to Algalord, but the Nordic Warrior sacrificed his life to kill him, and the Emerald Sword is presumably lost forever.
And again in the sequel, the Dark Secret Saga, though slightly happier: Dargor and his companions find the Seventh Black Book, they are winning the final battle with Nekron and his demonic army, but in the end Dargor has to sacrifice himself to transcend to godhood and battle Nekron for the rest of eternity to save the kingdom.
The Dream of Gerontius ends with the Angel dutifully delivering the Soul to Purgatory for cleansing. It's not as bad as Hell - there are other angels there whose sole duty, willingly undertaken, is to make the experience less unpleasant, and eventual release to eternal bliss is absolutely guaranteed - but Gerontius still has to be left behind as the Angel returns to his place in the courts of glory; and the song of the souls in Purgatory is, at best, resigned.
T-ara's Cry Cry and Lovey Dovey movie music. The protagonist, Jiyeon lost her father and unknowingly lives with the killer, a bounty hunter. When her love's toward him grows, she finally learn the truth for one of her father's goon, which ran away without even helping any further. The goon then takes her away from the bounty hunter and throws her on a street nowhere. She is forced to change her face, thanks to so many injuries and live with a girl who saved her life. When she finally meets the killer, he did not recognizes her, depressing her even more. He finally recognizes her, but died trying to save her from that goon. The goon did died. Sadden by this, Jiyeon commits suicide.
Haruka Shimotsuki's and Nao Hiyama's collaborative Tindharia world vocal albums, which tell stories about a fantasy world called Tindharia, all have such a ending:
In Tindharia no Tane, the heroine Parsley ends up giving up her life to change the laws that rule the world, while main character, Salt, is left behind taking care for the world she left behind.
In Griotte no Nemurihime one of the twins that serve as main characters to the story, Rosa, is absorbed into a song that makes her disappear forever. The story ends with the main characters throwing into the sea a crystal that contained her final song, which expressed her feelings for her sister, Citra.
And finally, in Koboreru Suna no ARIA, which serves as a prequel to Griotte no Nemurihime, the heroine Seshiara is forced to sing for years in an attempt to restore the weakened sunlight, until the point in which she falls dead from exhaustion. Her husband Forgeit learns about this much later, and this causes him to become crazy and turn into the antagonist for Griotte. The finale of the album shows Forgeit dying as apparently, Seshiara's spirit comes to take him to the afterlife. Unfortunately, both were doomed by the canon...
"I Remember Me" by Silver Jews is about a man who is hit by a truck and falls into a coma from which isn't expected to wake up. He does wake up, but by this time his girlfriend has found someone else.
Pepe Deluxé's Queen of the Wave ends with the destruction of Atlantis and the deaths of the protagonists along with the villain. This is only tempered by the fact that one Noah-figure and his family escaped the destruction: humanity will rebuild "and the future will sparkle again".
Vocaloid producer mothy's "Kept Waiting for a Response" might not be canon to the Story of Evil, but as one of the endings mothy originally had in mind and closely tied to what he eventually went with it certainly qualifies. Riliane fully regrets her actions, is redeemed and dies a happy death among the children she raised in an orphanage, but her twin Allen and many other people died because of her and in the end, she can't really get her one last wish- she wishes to have a response to a letter she sent years ago... but the letter was to the already dead Allen and she knows that, even as a boy gives her a fake reply and she smiles and thanks him.
"Graduation Trip" by Bowling for Soup has a heartbreaking yet oddly sweet story about first love, the singer detailing how he met and fell in love with a girl on a school trip.
The Gold Rush era folk-song "Sweet Betsy From Pike" tells the story of the titular woman and her husband Ike traveling to California. They survive numerous hardships, almost starve, fend off hostile Indians and successfully arrive.. only in the last verse to get a divorce.